Continuity mistake: In episode 2.09 of related show "Arrow," during the day the particle accelerator is activated, Barry spends his time with Oliver, Felicity, and Diggle in Starling City. He arrives back in Central City just in time to see the particle accelerator activated, and he is in his lab because he was too late and missed the line at S.T.A.R. Labs. In episode 101 of "The Flash," Barry was never in Starling City during the day the particle accelerator was activated, and he and Iris actually attended the event. (00:02:10 - 00:11:30)
Continuity mistake: At the facility test while Barry is about to run the sun changes between shots.
Things You Can't Outrun - S1-E3
Continuity mistake: As Barry is going up the stairs in the police station and says he doesn't want a museum dedicated to him, a man and a woman are walking down the stairs. However, a second later, the shot has changed and the man is now a different person and the woman has gone completely.
Things You Can't Outrun - S1-E3
Other mistake: When Cisco and Cailtin call Barry to tell him about the man with the gun, Cailtin says he has a gun. Cut to the cops pursuing him, the perp shoots at the cops, and one of them seems surprised that he has a gun. There's no way Caitlin could have known about the gun without the cop knowing (which would presumably have been relayed over police communications).
Going Rogue - S1-E4
Character mistake: "Restricted" is misspelled on the sign in the Utility Storage cage. (00:20:20)
Going Rogue - S1-E4
Deliberate mistake: When Capt. Cold is about to shoot Joe in the train station, Eddy "shoots" a pillar next to him to make him run. Eddy then comes from behind the pillar that got shot with no cuts. He would have had to been on the complete opposite side to shoot the pillar where it was hit. (00:32:50)
Suggested correction: I watched the scene several times and nothing indicates the pillar was shot from the left side. It looks like the pillar was shot from behind (which is why there's no hole on the side or front), exactly where Eddie would have been standing.
Going Rogue - S1-E4
Continuity mistake: When Captain Cold shots Joe with the ice gun, he hits Flash instead, in the left side of his abs, but in the next shot the ice switches sides.
Power Outage - S1-E7
Continuity mistake: Barry examines the charred corpse in the morning, telling Joe and Eddie he hopes they skipped breakfast. He goes to Star and Cisco does facial reconstruction. They get the alert about the power plant, and when Barry arrives, it's nighttime.
Continuity mistake: As the detectives are talking to their captain about the bank robbery, in a shot from behind the captain he takes his hands off his food and clasps them in front of him. The shot cuts to his front as he starts talking, and he moves his hands and clasps them again.
Revenge of the Rogues - S1-E10
Plot hole: During the fight at sundown, Cold gets a hit on Flash and he goes down. Eddie takes a shield and goes to help. But Flash was in the middle of the street with no obstacles around, and it's implausible that Eddie could have gotten to him without Cold or Heat seeing him.
Fast Enough - S1-E23
Continuity mistake: When Eddie is dead, his eyes are closed. But in a close up shot of him, his eyes are opened. Then when he's being pulled into the wormhole, they're closed again.
Fast Enough - S1-E23
Continuity mistake: When Ronnie and Caitlin are getting married the sun changes between shots.